Methods and systems for analyzing engine unbalance conditions

ABSTRACT

Methods and systems for analyzing engine unbalance conditions are disclosed. In one embodiment, a method includes receiving vibrational data from a plurality of locations distributed over an engine and a surrounding engine support structure, and inputting the vibrational data into a neural network inverse model. The neural network inverse model establishes a relationship between the vibrational data and an unbalance condition of the engine, and outputs diagnostic information indicating the unbalance condition of the engine. In a further embodiment, a method further includes subjecting the vibrational data to a Fast Fourier Transformation to extract a desired once per revolution vibrational data prior to input to the neural network inverse model.

FIELD OF THE INVENTION

The present disclosure relates to methods and systems for analyzingengine unbalance conditions, and more specifically, to neural networksystems for analyzing linear and non-linear vibrational phenomena.

BACKGROUND OF THE INVENTION

Many types of industrial machines include rotating components that maysuffer from unbalance conditions. During operation, such unbalanceconditions may cause undesirable vibrational effects throughout themachine. For example, it is known that unbalance conditions in aircraftengines may result in unwanted acoustic noise and structural vibrationsthroughout the aircraft. It is therefore desirable to characterize andcontrol unbalance conditions of rotating components of aircraft engines,as well as the unbalance conditions of the rotating components othertypes of industrial machines.

Considerable efforts have been devoted to the diagnosis and managementof engine unbalance conditions. One conventional method practiced byengine manufacturers is to modify the locations where engine vibrationsmay be transferred to the aircraft structure in order to reducestructurally transmitted vibrations, including the installation and useof damped bearings and vibration isolators. Another conventional methodis to regularly balance the rotating components of aircraft enginesusing weights at specific locations, similar to that common practice ofbalancing automotive wheels. Still other methods of diagnosing andmanaging engine unbalance conditions may involve computational analysisof vibrational data using software algorithms that strive tomathematically model and characterize such data. Such algorithms maythen be used for the computational prediction and development ofappropriate vibrational damping solutions (e.g. the selection andlocation of balancing weights). Such methods include, for example, thosemethods and systems disclosed in U.S. Pat. No. 6,027,239 issued toGhassaei, U.S. Pat. No. 5,586,065 issued to Travis, U.S. Pat. No.5,313,407 issued to Tiernan et al., and U.S. Pat. No. 5,172,325 issuedto Heidari.

Although desirable results have been achieved using such prior artmethods and systems, there is room for improvement. For example, onepossible weakness of at least some prior art algorithms is that suchalgorithms employ linear equations to characterize the enginevibrational data, even though the vibrational data may includesignificant non-linear components. Possible sources of non-linearvibrational data in an aircraft may include engine rotor shaft couplingmisalignments, imbalances in the compressor and turbine stages of theengine, squeeze film bearings, and inner shaft bearings that couple thehigh and low rotors, structural members and joints, attachmentcomponents, and other possible sources. Non-linear components ofvibration from such sources may not be adequately modeled using priorart linear analysis methods.

Another possible drawback of most of the prior art methods and systemsis that such methods typically strive to minimize the vibratorydisplacement of only a limited number of locations (commonly only twolocations) on the aircraft engine. Even though the locations may becarefully chosen in an attempt to reflect the general condition of theaircraft engine, the practice of forcing only a limited number oflocations to be at their lowest possible overall vibrational level doesnot guarantee that vibratory energy cannot flow into the wing andfuselage through other flow paths. Therefore, novel methods and systemsfor analyzing engine unbalance conditions that at least partiallymitigate these adverse characteristics of the prior art methods would beuseful.

SUMMARY OF THE INVENTION

The present invention is directed to methods and systems for analyzingengine unbalance conditions. Apparatus and methods in accordance withthe present invention may advantageously provide improvedcharacterization and diagnosis of engine vibrational data, particularlyvibrational data including significant non-linear components, andparticularly for applications where numerous alternate flow paths forvibrational energy may impart undesirable acoustic (cabin noise) orstructural fatigue effects.

In one embodiment, a method of analyzing an engine unbalance conditionincludes receiving time domain vibration data from a plurality oflocations distributed over at least one of an engine and/or asurrounding engine support structure, and inputting the vibrational datainto a neural network inverse model. The neural network inverse modelthen establishes a relationship between the vibrational data from theplurality of locations and an unbalance condition of the engine, andoutputs diagnostic information from the neural network inverse model,the diagnostic information indicating the unbalance condition of theengine. In a further embodiment, a method further includes subjectingthe vibrational data to a Fast Fourier Transformation to extract adesired once per revolution vibrational data prior to input to theneural network inverse model. In another embodiment, a method includespreprocessing the vibrational data to transform it into wavelet basisfunctions to enhance extraction of meaningful vibration and acousticnoise features and relationships.

In a further embodiment, the vibration data is not used to ‘balance’ theengine by reducing the vibration transducer signatures to their lowestlevel, but is used instead to detect relationships between parametersthat are related to energy transmission. As noted by Travis (U.S. Pat.No. 5,586,065), conventional balance methods do not always address theenergy that can flow through alternative energy paths that are notrepresented by the accelerometer locations. The neural network approachcan be used to detect parameter relationships that define new andnon-obvious metrics for the energy transmission into the fuselage,metrics that provide more meaningful information than the arbitrarilylow level of vibration sensors on the engine. Examples are: differencesbetween vibration amplitudes fore and aft on the engine, phase angledifferences between accelerometers, differences between vibrationphasing from one engine to another, and combinations/permutationsthereof.

In a further embodiment, the balancing of the engine can be performedusing non-traditional input parameters such as cabin accelerometers,cabin microphones, and component structural fatigue measurementsprovided by accelerometers, with or without engine accelerometer data.As before, these data sets may be time domain or frequency domain inputsto the artificial neural network.

BRIEF DESCRIPTION OF THE DRAWINGS

The preferred and alternative embodiments of the present invention aredescribed in detail below with reference to the following drawings.

FIG. 1 is a flow chart of a method of analyzing an engine unbalancecondition in accordance with an embodiment of the invention;

FIG. 2 is a side cross-sectional view of a representative aircraftengine and aircraft equipped with vibrational and acoustic sensors inaccordance with an embodiment of the invention;

FIG. 3 is a schematic view of a set of possible input sources of enginevibrational data in accordance with a further embodiment of theinvention;

FIG. 4 is a schematic view of a process for evaluating and assessingperformance of a neural network in accordance with another embodiment ofthe invention;

FIG. 5 is a schematic view of a typical multilayer perceptron neuralnetwork in accordance with yet another embodiment of the invention;

FIG. 6 is a schematic view of another multilayer perceptron neuralnetwork in accordance with another alternate embodiment of theinvention; and

FIGS. 7A through 7C show representative systems for analyzing enginevibrational data in accordance with further embodiments of the presentinvention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention relates to methods and systems for analyzingengine unbalance conditions, and more specifically, to neural networksystems for analyzing linear and non-linear vibrational phenomena. Manyspecific details of certain embodiments of the invention are set forthin the following description and in FIGS. 1-7 to provide a thoroughunderstanding of such embodiments. One skilled in the art, however, willunderstand that the present invention may have additional embodiments,or that the present invention may be practiced without several of thedetails described in the following description.

In brief, methods and systems in accordance with the present inventionutilize equations based on the neural network approach to optimizinglinear and nonlinear systems. Such methods and systems may be used toanalyze sensor data and diagnose the unbalance state of an aircraftengine, to evaluate the practicality of the technology for enginebalancing, and to evaluate the robustness of the approach when facedwith nonlinearities which make present state of the art engine balancingtechniques break down. Embodiments of methods and systems according tothe present invention employ an inverse model that can analyze sensordata and diagnose the unbalance state of the engine. Several neuralnetwork methods, including multilayer perceptron (MLP) and supportvector machines (SVMs), may be used in the inverse model. The methods todetermine the inverse model design parameters, often referred to as“training”, includes but is not limited to those commonly employed inthe field such as back propagation, conjugate gradient, extended Kalmanfilter (EKF), and sequential minimal optimization.

FIG. 1 is a flow chart of a method 100 of analyzing an engine unbalancecondition in accordance with an embodiment of the invention. In thisembodiment, the method 100 includes inputting raw vibrational data 102which may be provided by sensors (e.g. accelerometers or microphones)mounted on portions of an aircraft engine or airframe structures. Theraw vibrational data (or time domain data) are subjected to a FastFourier Transform (FFT) 104 which may extract the desired once perrevolution vibrational data. The method 100 further includes outputting(or extracting) the FFT-processed vibrational data 106, preferablyincluding a vibrational amplitude 108 at a specified engine rotationalfrequency 110. As further shown in FIG. 1, the FFT-processed vibrationaldata in complex form (amplitude and phase) are used as the input 106into a neural network inverse model 112, which in turn outputsvibrational diagnostic information 114, as described more fully below.The vibrational diagnostic information may include fan unbalance andangular location data, low pressure turbine (LPT) unbalance and angularlocation data, and other diagnostic information.

In one aspect, the Fast Fourier Transform 104 may be performed using atechnique known as order tracking. In brief, order tracking frames theFFT block size such that leakage effects may be reduced or eliminatedand enabling the true once per revolution response amplitude at theengine rotation frequency to be extracted. All other spectral content(at other frequencies) may be discarded. Alternately, the time-domaindata may transformed into other basis function spaces, such as Wavelets116, to yield information contained in feature vectors, that are thenused as the input 106 into a neural network inverse model 112.Alternately, the Fast Fourier Transform 104 or Wavelet Transform 116 maybe eliminated, and the time-domain vibrational data 102 may be inputdirectly into the neural network inverse model 112. The use of the rawtime-domain data in conjunction with filtering, correlation, and orderreduction methods commonly used in practice is a more general approachthat does not presume periodicity and may be better suited for someengine balance applications.

FIG. 2 shows a side cross-sectional view of a representative aircraftengine 200 equipped with vibrational sensors, including flangeaccelerometers 202, a strut accelerometer 204, and a tail coneaccelerometer 206 used to obtain measurements affecting structuralfatigue life. FIG. 2 also shows a cross-section of a representativeaircraft frame 214 equipped with vibrational and acoustic sensors,including cabin and structure accelerometers 212, cabin noise acousticsensors (typically microphones) 210, and surface accelerometers 208 usedto obtain measurements affecting structural fatigue life. The aircraft214 shown in FIG. 2 is generally representative of a commercialpassenger aircraft, including, for example, the 737, 747, 757, 767, and777 models commercially-available from The Boeing Company. The inventiveapparatus and methods disclosed herein, however, may also be employed inany other types of aircraft, such as rotary aircraft or manned militaryaircraft, including those described, for example, in The IllustratedEncyclopedia of Military Aircraft by Enzo Angelucci, published by BookSales Publishers, September 2001.

As shown in FIG. 2, the aircraft 214 includes one or more engines (orpropulsion units) 200 operatively coupled to a fuselage 250, wingassemblies 252 (or other lifting surfaces), a tail assembly 254, alanding assembly 256 (not visible), a control system 258 (not visible),and a host of other systems and subsystems that enable proper operationof the aircraft 214. In general, except for the vibrational monitoringsystem described more fully below, the various components and subsystemsof the aircraft 214 may be of known construction and, for the sake ofbrevity, will not be described in detail herein.

FIG. 3 is a schematic view of a set of engine variables 300 that mayimpact the raw engine vibrational data 102 used by the method 100 (FIG.1). As shown in FIG. 3, the engine variables 300 may include enginerotational speed w, unbalanced mass mr, and unbalanced location wt. Therepresentative aircraft engine 200 (FIG. 2) may be operated at variousoperating conditions by adjusting the various engine variables 300,thereby providing the raw sensor data 102 that are input into methods inaccordance with the present invention, including the embodiment (method100) shown in FIG. 1.

Generally, at a given engine rotational speed w (or RPM), engineunbalances may produce a vibrational response at several sensorlocations on the aircraft engine and surrounding structure. Methods inaccordance with the present invention may include training the neuralnetwork inverse model 112 (FIG. 1) (e.g. using applied trial weights)until the model has established a mapping or correlation between appliedengine unbalance and the measured responses of the engine. Since engineunbalance can vary in magnitude, angular location, and balance plane(e.g. of the fan or low pressure turbine), it is preferably to exposethe model to responses from a variety of unbalance conditions. Aftertraining, the model may then be directly applied to subsequent enginesfor which a balance solution is sought, preferably with no furthertraining required. Further accuracy of the model to match specificengine-airplane installations may be obtained by repeating the trainingprocess either on-board or off-board using data gathered during flightoperations each time new balance weights are added to an engine.

In general, adequate training of the neural network inverse model 112requires test data in the design stage of the condition monitoringsystem for training the model, as well as independent test data forvalidation of the model and overall method. Such data may be acquired byrepeated trails in which experimental unbalance weights are deliberatelyplaced on various components (e.g. the fan and low pressure turbine) ofthe engine at various angular locations and in varying amounts ofunbalance weight, and is the preferred training method.

Since it may be unknown how much data is needed to adequately train theneural network model, and since large amounts of test data from a singleengine with many unbalance weights applied may be unavailable, analternate approach to using experimentally-generated training data is todevelop an empirical engine-airframe to generate the required responsesto unbalance inputs. Such empirical models may be created using limitedtest cases of actual jet engine unbalance conditions and experimentallyobserved responses of vibration at senor locations, vibration atinstrumented component locations, and/or acoustic noise levels atvarious locations. Using such an empirical model approach may provide alarge amount of sufficiently accurate data for the purpose of thisinvention because the unbalance and responses relationship in theempirical engine model can be made to match exactly at theexperimentally generated test points, and then transition continuouslyand smoothly between the test points, as would be expected based on thephysical constraints of such a system. Other known methods ofempirically modeling aircraft engines that may be suitable forevaluation of the effect of the deliberate introduction of varyingdegrees of system nonlinearity in a controlled manner include, forexample, those methods disclosed in “Experience in Rotor Balancing ofLarge Commercial Jet Engines” authored by J. L. White, M. A. Heidari,and M. H. Travis, and published at SEM Proceedings of the 13^(th)International Modal Analysis Conf., Vol. II, 1995, pp. 1338-1344, whichpublication is incorporated herein by reference.

For example, in one embodiment, an empirical engine may be created usingan Influence Coefficient (IC) matrix approach from actual enginevibration test data. Using the IC approach, the vibration response ofthe engine to engine unbalance can be represented using the followingcomplex matrix expression:X(f)=R(f)F   (1)Where X(f)=complex column vector of n sensor responses at a given enginefrequency f

-   -   R(f)=experimentally determined complex IC matrix of dimension        n×2    -   F=complex unbalance vector that represents unbalances on the Fan        and LPT

In one representative example, if two engine vibration sensors areemployed, then n is equal to 2, and the IC matrix is a 2×2 matrix ofcomplex numbers at any given frequency. Typically, a plurality of steadystate engine RPM operating point frequencies (e.g. ten or more) forengine balancing over the climb and cruise range of the engine areemployed. Preferably, the influence coefficients represent typicaldynamic response characteristics in amplitude and phase versus engineRPM.

When balancing a jet engine on an aircraft, the amount of inherent orresidual unbalance on the engine is the unknown property. Trial weightscan be added to the engine, and the responses can be observed, but theforces acting on the engine to make those responses are unknown sincethey are a combination of applied and residual unbalances. Accordingly,during training of a neural network inverse model, an engine that hasexisting residual unbalances acting on it, as well as applied trialweight unbalances, may be employed. The neural network inverse model isnot given information about the residual unbalance, and must establishthe relationship between measured responses and trial weight unbalancesonly. The creation of an empirical engine with both residual and trialweights acting on it includes expanding the force column vector inEquation (1) above to consist of two column vector components, theresidual unbalance, and the applied unbalance, that together create thenet applied unbalance, as follows:F _(net) =F _(residual) +F _(trial)   (2)

The above-referenced techniques may be incorporated into a process fortraining a neural network inverse model. In brief, the neural networkinverse model may be trained by adjusting model parameters such thatapplication of a set of inputs matches a desired set of outputs. Onesuch training method is called the “back-propagation” algorithm. Theback-propagation algorithm can train multi-layer feed-forward neuralnetwork inverse models with differentiable transfer functions to performfunction approximation. Once the model has learned the engine behavior,whether it is linear or non-linear, any subsequent vibration data thatis supplied to the model may characterize the state of residualunbalance on the engine, which may then be used to balance the engine.

For example, FIG. 4 is a schematic view of a process 400 process forevaluating and assessing performance of a neural network inverse modelin accordance with another embodiment of the invention. In thisembodiment, the process 400 includes providing vibration data at aplurality of locations on the aircraft engine, specifically, at a fanvibration sensor 402 and a low pressure turbine sensor 404. Trial engineunbalance data are also are provided, including trial fan unbalance data406 and trial LPT unbalance data 408.

The input data (vibration data and trial unbalance data) are summed forthe fan data 410 and for the LPT data 412, respectively, resulting innet fan unbalance data 414 and net LPT unbalance data 416. These netdata 414, 416 are transmitted into an empirical engine module 418, suchas an IC-based empirical model, which then combines these inputs withempirically-derived influence coefficients and outputs raw enginevibrational data 420, including raw engine vibrational data for the fan(or first) sensor 422 and the LPT (or second) sensor 424.

As further shown in FIG. 4, these raw engine vibrational data 422, 424are then input into the neural network inverse model 426. The trial fanunbalance data 406 and the trial LPT unbalance data 408 are alsoprovided to the neural network inverse model 426. As further shown inFIG. 4, the neural network inverse model then outputs predicted fanunbalance data 428 and predicted LPT unbalance data 430. These predictedunbalance data 428, 430 may then be analyzed and compared withanticipated or known outputs. Internal parameters of the neural networkinverse model may then be adjusted, and the above-referenced acts of theprocess 400 shown in FIG. 4 may then be repeated to evaluate and assessthe performance of the model.

The input to the neural network inverse model is vibration amplitude andphases of the two accelerometers (phase is relative to a once perrevolution tachometer signal). The outputs of the neural network inversemodel are unbalances on the shaft that it detects, which are alsocomplex numbers in amplitude and angular orientation (angle relative toan index on the shaft). Since the input and output to the neural networkinverse model are complex numbers, then the neural network inverse modelitself is a complex mapping. In other words, the neural network inversemodel is trained to establish the complex relationship between complexengine vibration response and complex unbalances acting on the engine atseveral locations.

A neural network inverse model may not be a generic model that can beapplied to any subsequent engine with different residual unbalance.Typically, training the neural network inverse model using trial weightswill establish a unique mapping that is biased by the residual engineunbalance that is present in the engine used to perform the training.There are, however, several analytical approaches to convert a uniquelytrained neural network inverse model into a generic neural networkinverse model that may be used for diagnosing other engines.

Generally, training of neural networks can be made more efficient if thedata (both the network input and output) can be scaled beforehand. Oneapproach for scaling network inputs and targets is to normalize the meanand standard deviation of the training set, which normalizes the inputsand targets so that they will have zero mean and unity standarddeviation. If this preprocessing approach is employed for the trainingset data, then whenever the trained network is used with new inputs,such new inputs should be preprocessed with the same means and standarddeviations that were computed for the training set. The outputsgenerated from these preprocessed inputs may also be converted back intothe same units that were used for the original targets.

Neural networks are generally known for their function approximation andpattern recognition performance. Several differing neural networkapproaches to the engine unbalance detection problem may be employed.For example, an approach known as backpropagation is the most commonmethod used in the training of feedforward neural networks (also knownas multilayer perceptron—MLP) with differentiable transfer functions.For example, FIG. 5 is a schematic view of a typical MLP neural network500 in accordance with yet another embodiment of the invention. In thisembodiment, the MLP neural network 500 includes an input layer 510having a plurality of inputs 512, a first hidden layer 520 including aplurality of first differentiable transfer functions 522, and finally,an output layer 530 including a plurality of outputs 532. Similarly,FIG. 6 is a schematic view of an MLP neural network 600 in accordancewith an alternate embodiment of the invention. In this embodiment, theMLP neural network 600 includes an input layer 610 having a plurality ofinputs 612, a first hidden layer 620 including a plurality of firstdifferentiable transfer functions 622, a second hidden layer 630including a plurality of second differentiable transfer functions 632,and finally, an output layer 640 including a single output 642.

Another potential approach is an algorithm called extended Kalman filter(EKF) as disclosed, for example, in “Neurocontrol of nonlinear dynamicalsystems with Kalman filter trained recurrent networks” by G. V.Puskorius and L. A. Feldkamp (Neural Networks, IEEE Transactions on,vol. 5, pp. 279-297, March 1994), and “Decoupled extended Kalman filtertraining of feedforward layered networks” by G. V. Puskorius and L. A.Feldkamp (Neural Networks, Proceedings of IJCNN-91-Seattle InternationalJoint Conference on, vol. 1, pp. 771-777, 1991).

In one embodiment, a Node Decoupled Extended Kalman Filter (DEKF) may beemployed as a natural simplification of the global extended Kalmanalgorithm (GEKF) by ignoring the interdependence of mutually exclusivegroups of weights, thereby allowing the computational complexity of EKFto be adjusted to the low requirements of the computational resources(see “Node decoupled extended Kalman filter based learning algorithm forneural networks” by S. Murtuza and S. F. Chorian, Intelligent Control,Proceedings of the 1994 IEEE International Symposium on, pp. 364-369,1994). Although the DEKF is always computationally less demanding thanthe GEKF, current computer speeds and memory sizes have now made theglobal EKF feasible for many practical problems. An advantage of the EKFapproach over the Standard BackPropagation (SBP) approach is that,generally, EKF may often produce results comparable to SBP but withsignificantly fewer presentations of training data and less overalltraining epochs.

Given a network with M weights and N_(L) output nodes, the weightsupdate for a training instance at the time step n of GEKF is given by:$\begin{matrix}{{{A(n)} = \left\lbrack {{R(n)} + {{H^{\prime}(n)}{P(n)}{H(n)}}} \right\rbrack^{- 1}},} & (3) \\{{{K(n)} = {{P(n)}{H(n)}{A(n)}}},} & (4) \\{{{\hat{W}\left( {n + 1} \right)} = {{\hat{W}(n)} + {{K(n)}{\xi(n)}}}},} & (5) \\{{{P\left( {n + 1} \right)} = {{P(n)} - {{K(n)}{H^{\prime}(n)}{P(n)}} + {Q(k)}}},} & (6) \\{{{P(0)} = {\frac{1}{\eta_{p}}I}},{{R(n)} = {\eta_{r}I}},{{Q(k)} = {\eta_{q}{I.}}}} & (7)\end{matrix}$

In the above equations, R(n) is a diagonal N_(L)-by-N_(L) matrix, whosediagonal components are equal to or slightly less than 1. H(n) is anM-by-N_(L) matrix containing the partial derivatives of the output nodesignals with respect to the weights. P(n) is an M-by-M matrix defined asthe approximate conditional error covariance matrix. A(n) is aN_(L)-by-N_(L) matrix that we refer to as the global scaling matrix.K(n) is an M-by-N_(L) matrix containing the Kalman gains for theweights. Ŵ(n) is a vector of length M containing the all the weightsvalues. ξ(n) is the error vector of the network's output layer. Whilethe motivation for the use of artificial process noise in equation (6)was, to avoid numerical difficulties, we have found in addition that itsignificantly enhances the performance of the GEKF algorithms in termsof rate of convergence, avoidance of local minimum and quality ofsolution.

Another possible approach for the neural network inverse model is knownas Support Vector Machines (SVMs) algorithms, as disclosed, for example,in “Support vector machines for classification and regression” by S. R.Gunn (Technical Report ISIS-1-98, Department of Electronics and ComputerScience, University of Southampton, 1998), “A tutorial on support vectormachines for pattern recognition” by C. Burges (Data Mining andKnowledge Discovery, 2(2): 121-167, 1998), “Libsvm: a library forsupport vector machines (version 2.3)” by C. Chang and C. Lin., and“Training feed-forward networks with the extended Kalman algorithm” byS. Singhal and L. Wu, (Proceedings of International Conference onAcoustics, Speech and Signal Processing (ICASSP-89), vol.2, pp.1187-1190, 1989).

In one embodiment, a support vector machine problem may be given thetraining samples {(x_(i), d_(i))}_(i=1) ^(N), where x_(i) is the inputvector, d_(i) is the corresponding target output, find the Lagrangemultipliers {α}_(i=1) ^(N) that maximize the objective function:$\begin{matrix}{{Q(\alpha)} = {{\sum\limits_{i = 1}^{N}\alpha_{i}} - {\frac{1}{2}{\sum\limits_{i = 1}^{N}{\sum\limits_{j = 1}^{N}{\alpha_{i}\alpha_{j}d_{i}d_{j}{K\left( {x_{i},x_{j}} \right)}}}}}}} & (8)\end{matrix}$subject to the following constraints: $\begin{matrix}{{{\sum\limits_{i = 1}^{N}{\alpha_{i}d_{i}}} = {{0\quad{and}\quad 0} \leq \alpha_{i} \leq C}},{i = 1},2,\ldots\quad,N} & (9)\end{matrix}$where C is a user-specified parameter. The K(x_(i), x_(j)) is the kernelfunction which maps the multidimensional input space (nonlinearlyseparable patterns) into a new feature space with higher dimension wherepatterns are linearly separable. This optimization problem may be solvedwith quadratic programming to provide an optimized Lagrange multiplier.A weight vector may then be determined according to the followingequation: $\begin{matrix}{W_{o} = {\sum\limits_{i = 1}^{N}{\alpha_{o,i}d_{i}{\varphi\left( x_{i} \right)}}}} & (10)\end{matrix}$where φ(x_(i)) is the image induced in the feature space due to x_(i). Asupport vector machine output y becomes $\begin{matrix}{y = {\sum\limits_{i = 1}^{N}{\alpha_{i}d_{i}{\varphi^{T}(x)}{{\varphi\left( x_{i} \right)}.}}}} & (11)\end{matrix}$The SVM technique may be applied to solve this regression problem, whichis support vector regression (SVR). Given the measurement from thesensors, SVM attempts to diagnose the mass imbalance on the engine.

A variety of metrics may be used to allow error to be quantified inorder to evaluate the various analytical approaches to the neuralnetwork inverse models. For example, in one embodiment, the results ofthe residual unbalance estimates produced by the neural network inversemodel may be compared to the known residual unbalances that had beenapplied to the IC engine model, and attempted to compute the errorbetween them. But error in the vector unbalance estimates may bedifficult to quantify, since errors can occur in both magnitude andangular orientation. For example, an estimate of 1 ounce inch at 0degrees that should have been 1 ounce inch at 90 degrees is a largeerror in terms of the vector difference, but in terms of the effect onthe engine response such an error could be small and in the noise levelof the data.

Alternately, a potentially more useful and revealing metric forevaluating error may be to apply the neural network inverse modelderived corrective balances to the original IC model as a trial weight,while retaining the original residual unbalances. By comparing theresponse of the IC engine with these corrective balance weights appliedto the response without these weights, the net improvement can beestablished. If effective, the neural network inverse model solutionshould produce low or nearly zero vibration response magnitudes. Errorsmay produce less than ideal engine responses, and may make the vibrationworse. Since the magnitudes of the vibration responses are typically ofprimary interest, then this method of error estimation may also besimpler to conduct.

Error detection on the validation set within the training itself mayalso be monitored during the training process. When the neural networkbegins to overfit the data, the error on the validation set willtypically begin to rise. Thus, when the validation error increases for aspecified number of iterations, the training may be stopped, and thenetwork weights at the minimum of the validation error may be returned.

The above-described methods based on the neural network approach tooptimizing linear and non-linear vibrational solutions may be embeddedin an integrated engine balancing system that may include sensors,signal conditioning algorithms, engine balance software, and data andsolution display devices. Such systems may be integrated in ground basedengine test stands, self contained on-board aircraft systems, handheldportable maintenance systems, ground-based health management systems, orother architectural embodiments that permit the execution of the dataanalysis and extraction of information. For example, FIG. 7A is arepresentative system 700 for analyzing engine vibrational data inaccordance with still another embodiment of the present invention.Unless otherwise specified below, the components of the system 700 areof generally-known construction, and will not be described in detail.For the sake of brevity, only significant details and aspects of thesystem 700 will be described. As shown in FIG. 7A, in this embodiment,the system 700 includes a computer 702 having a central processing unit(CPU) 704 and a memory component 706. The memory component 706 mayinclude one or more memory modules, such as Random Access Memory (RAM)modules, Read Only Memory (ROM) modules, Dynamic Random Access Memory(DRAM) modules, and any other suitable memory modules. The computer 702also includes an input/output (I/O) component 708 that may include avariety of known I/O devices, including network connections, video andgraphics cards, disk drives or other computer-readable media drives,displays, or any other suitable I/O modules. A data bus 710 operativelycouples the CPU 704, memory component 706, and the I/O component 708.

The system 700 embodiment shown in FIG. 7A further includes a dataacquisition component 712 operatively coupled to the computer 702. Inthis embodiment, the data acquisition component 712 includes a pluralityof data acquisition sensors 714 that may be arrayed on a test article750 (e.g. FIG. 2) for the acquisition of mechanical vibrational data andacoustic noise data. The data acquisition component 712 is operativelycoupled to the computer 702 via a communication link 716. Thecommunications link 716 providing the means to communicate thevibrational and acoustic data in this embodiment may consist of one ormore methods generally used in the practice such as data buses, wirelessdata link, magnetic computer media, optical computer media, and anyother suitable means for transferring data from the test article to theprocessing computer 702.

As further shown in FIG. 7A, the system 700 further includes a controlcomponent 720 having a monitor 722 and a command input device 724 (e.g.a keyboard, an audio-visual input device, etc.). A second communicationlink 718 operatively couples the control component 720 to the computer702. The system 700 also includes an auxiliary output device 726 coupledto the computer 702 by a third communication link 728. The auxiliaryoutput device 726 may include a printer, a compact disk (CD) burner, astorage device, a communication port, or any other desired outputdevice.

In one aspect, a machine-readable medium may be used to store a set ofmachine-readable instructions (e.g. a computer program) into thecomputer 702, wherein the machine-readable instructions embody a methodof analyzing engine vibration data in accordance with the teachings ofthe present invention. The machine-readable medium may be any type ofmedium which can store data that is readable by the computer 702,including, for example, a floppy disk, CD ROM, optical storage disk,magnetic tape, flash memory card, digital video disk, RAM, ROM, or anyother suitable storage medium. The machine-readable medium, or theinstructions stored thereon, may be temporarily or permanently installedin any desired component of the system 700, including, for example, theI/O component 708, the memory component 706, and the auxiliary outputdevice 726. Alternately, the machine-readable instructions may beimplemented directly into one or more components of the computer 702,without the assistance of the machine-readable medium.

In operation, the computer 702 may be configured to perform one or moreof the aspects of the methods of analyzing engine vibration datadescribed above. For example, an operator 730 may input a commandthrough the command input device 724 to cause the data acquisitioncomponent 712 to obtain raw engine vibrational data as described abovewith reference to FIGS. 1-3. The test data sets may then be communicatedfrom the data acquisition component 712 to the computer 702. Thecomputer 702 may be configured to perform the above-described methods ofanalyzing the vibrational data or training the neural network inversemodel. For example, a set of software instructions may be stored in thecomputer 702 (e.g. in the memory component 706) that causes the rawengine vibrational data to be read into the memory component 706 andprocessed using the CPU 704 in accordance with the teachings herein,including one or more of the processes described above with respect toFIGS. 1-6. Alternately, one or more aspects of the various processesdescribed above may be implemented in the computer 702 using anysuitable programmable or semi-programmable hardware components (e.g.EPROM components).

Results of the analysis in accordance with one or more embodiments ofthe present invention may be transmitted via the data bus 710 to the I/Ocomponent 708. The results may also be transmitted to the controlcomponent 720 and to the auxiliary output device 726 via the second andthird communications links 718 and 728. The operator 730 may view theresults of the analysis method(s) on the control monitor 722, and maytake appropriate action, including revising analysis parameters andinputs, and continuing or repeating the one or more embodiments ofanalysis methods using different test data as desired.

In yet another embodiment shown in FIG. 7B, the computer 702, dataacquisition component 712, communications links 716 and 718, andauxiliary output device 726 are implemented within the test articleenvironment 750, such as in the engine compartment or other on-boardaircraft locations. The benefits of such an on-board implementation liesin the ability to provide timely engine unbalance information toaircraft operators and maintainers either on-board, or in the nearvicinity of the aircraft, in addition to the afore described advantagesof non-linear engine vibrational data analysis.

In yet another embodiment shown in FIG. 7C, the data acquisitioncomponent 712, a data storage device 740, and a communications link 716are implemented within the test article environment 750, such as in theengine compartment or other on-board aircraft locations. The vibrationaldata and acoustic data are made available to the computer 702 via acommunications link 716 commonly available in practice such as databuses, magnetic and optical computer media, wireless communicationlinks, and satellite-based and cellular-based aircraft data downlinkcommunication systems. The benefits of such an on-board data acquisitionimplementation lies in the ability to selectively acquire high qualityoperational test article data that will maximize the afore describedadvantages of non-linear vibrational data analysis, in addition toreducing the adverse effects of on-board computer weight and powersupply in comparison with the prior art methods.

Methods and systems for analyzing engine unbalance conditions mayprovide significant advantages over the prior art. For example,embodiments of methods including neural network inverse models inaccordance with the present invention may provide improvedcharacterization and diagnosis of engine vibrational data and acousticnoise data, particularly data including significant non-linearcomponents. Since neural network inverse models are equally applicationto both linear and non-linear vibrational problems, methods and systemsincorporating such models are better equipped to analyze vibrationaldata including non-linear components. Furthermore, embodiments ofmethods and systems in accordance with the invention may provideimproved engine balance solutions in comparison with the prior artmethods that target the reduction of vibrational displacement at onlytwo locations, particularly for applications where numerous alternateflow paths for vibrational energy may be significant.

It should be noted that the construction of an artificial neural networkusing back-propagation uses “input” and “output” terminology that arethe reverse of what would be viewed as input and output from an overallprocess. To be more precise, when using back-propagation, the vibrationdata from the sensors is the output to the artificial neural network,and the input is the unbalance. The desired solution, in this case theunbalance magnitudes and angular locations, are backpropagated, orsolved for. This terminology is consistent with the concept of neuronsand how neurons interact in a downstream sense. However, if one places acontrol volume around the entire process of acquiring data, supplying itto a neural network, and extracting useful information, the vibrationdata is the input to the control volume, and the output is the unbalanceinformation. This distinction is drawn so as to establish more preciseterminology for the claims, where an artificial neural network controlvolume, or ANNCV, shall refer to the entire data processing packagecontrol volume, irrespective of back-propagation or some other method ofinternal solution. The ANNCV shall be inclusive and independent ofwhether inverse back propagation models, Kalman filter Models, orSupport Vector Machine models are used.

While preferred and alternate embodiments of the invention has beenillustrated and described, as noted above, many changes can be madewithout departing from the spirit and scope of the invention.Accordingly, the scope of the invention is not limited by the disclosureof the preferred embodiment. Instead, the invention should be determinedentirely by reference to the claims that follow.

1-31. (canceled)
 32. A system for analyzing an engine unbalancecondition, comprising: a control component; an input/output devicecoupled to receive vibrational data; and a processor arranged to analyzethe vibrational data, the processor including: a first portion adaptedto receive vibrational data from a plurality of locations distributedover at least one of an engine and surrounding engine support structure;a second portion adapted to input the vibrational data into a neuralnetwork inverse model; a third portion adapted to establish arelationship between the vibrational data from the plurality oflocations and an unbalance condition of the engine using the neuralnetwork inverse model; and a fourth portion adapted to output diagnosticinformation from the neural network inverse model, wherein thediagnostic information indicates at least one of the unbalance conditionof the engine and information indicating the quantity and position ofcorrective engine balance weights needed to achieve desirablevibrational characteristics at the plurality of locations.
 33. Thesystem of claim 32, wherein the second portion is adapted to input thevibrational data in a time domain format into a neural network inversemodel.
 34. The system of claim 32, wherein the second portion is adaptedto input the vibrational data in a complex domain format into a neuralnetwork inverse model.
 35. The system of claim 32, wherein at least oneof the first, second, and third portions is adapted to subject thevibrational data to a Fast Fourier Transformation.
 36. The system ofclaim 32, wherein at least one of the first, second, and third portionsis adapted to extract a desired once per revolution vibrational data.37. The system of claim 32, wherein at least one of the first, second,and third portions is adapted to subject the vibrational data to aWavelet Transformation.
 38. The system of claim 32, wherein the thirdportion is adapted to establish a relationship between the vibrationaldata from the plurality of locations and an unbalance condition of theengine using at least one of a multilayer perceptron neural networkmodel, and a support vector machine neural network model.
 39. The systemof claim 32, wherein the third portion is adapted to establish arelationship between the vibrational data from a plurality of locationswithin one defined area to that of a plurality of locations withinanother defined area using at least one of a multilayer perceptronneural network model and a support vector machine neural network model.40. The system of claim 32, wherein the third portion is adapted to betrained including adjusting model parameters such that application of aset of inputs and outputs reaches a desired state of definition definedby acceptable error tolerances.
 41. The system of claim 32, wherein thethird portion is adapted to be trained including using vibrational datagenerated using an engine that is subject to at least one of residualunbalances and applied trial weight unbalances.
 42. The system of claim32, wherein the third portion is adapted to be trained including scalingthe vibrational training data prior to inputting into the neural networkinverse model.
 43. The system of claim 32, further including a memorycomponent operatively coupled to at least one of the control component,the input/output device, and the processor.
 44. The system of claim 32,further including a data acquisition component operatively coupled to atleast one of the control component, the input/output device, and theprocessor.
 45. The system of claim 44, wherein the data acquisitioncomponent includes a plurality of data acquisition sensors. 46-58.(canceled)